1. **State the problem:** Calculate the net present value (NPV) of a project where the initial investment includes the cost of a machine and installation, and the project generates incremental after-tax cash flows over three years. The required rate of return is 13.0%. 2. **Formula for NPV:** $$\text{NPV} = -\text{Initial Investment} + \sum_{t=1}^n \frac{\text{Cash Flow}_t}{(1 + r)^t}$$ where $r$ is the required rate of return and $t$ is the year. 3. **Calculate initial investment:** $$\text{Initial Investment} = 27457 + 4624 = 32081$$ 4. **Calculate present value (PV) of each cash flow:** - Year 1: $$\frac{9903}{(1 + 0.13)^1} = \frac{9903}{1.13}$$ - Year 2: $$\frac{13581}{(1 + 0.13)^2} = \frac{13581}{1.13^2}$$ - Year 3: $$\frac{16949}{(1 + 0.13)^3} = \frac{16949}{1.13^3}$$ 5. **Calculate each PV value:** - Year 1: $$\frac{9903}{1.13} \approx 8761.95$$ - Year 2: $$\frac{13581}{1.2769} \approx 10636.15$$ - Year 3: $$\frac{16949}{1.4429} \approx 11745.15$$ 6. **Sum of PVs:** $$8761.95 + 10636.15 + 11745.15 = 31143.25$$ 7. **Calculate NPV:** $$\text{NPV} = -32081 + 31143.25 = -937.75$$ 8. **Round to nearest dollar:** $$\text{NPV} \approx -938$$ **Final answer:** The net present value of the project is -938.